Sort of. Once upon a time serious Sweet pea growers did indeed spend hours removing the tendrils. This was done so that the plant put its energy into producing more flowers with longer stems. It is not compulsory though.

If you want the plants to climb up sticks or mesh or something, don't cut the tendrils off - that's what they use to scramble up other plants or supports you've provided. What's critical is to remove faded flowers immediately so they don''t set seed, which they do rather quickly. Removing tendrils is likely something that growers for competitive flower shows will have done, or professional growers producing flowers for sale.